HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.

Find the symbolic form of the following switching circuit, construct its switching table and interpret it.

Simplify the following circuit so that the new circuit has minimum number of switches. Also, draw the simplified circuit.

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

Which of the following is not a statement?

The false statement in the following is ______.

State the truth Value of x² = 25

Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”

Check whether the following matrix is invertible or not:

`[(cos theta, sin theta),(-sin theta, cos theta)]`

Express the following equations in matrix form and solve them by the method of reduction:

x + 2y + z = 8, 2x + 3y - z = 11, 3x - y - 2z = 5.

In ΔABC, prove that `tan((A - B)/2) = (a - b)/(a + b)*cot  C/2`.

Show that:

`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`

Select the correct option from the given alternatives:

In ΔABC if c² + a² – b² = ac, then ∠B = ____.

The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______

With usual notations, prove that `(cos "A")/"a" + (cos "B")/"b" + (cos "C")/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")`

Find the principal solutions of tan x = `-sqrt(3)`

In ΔABC, if a cos A = b cos B, then prove that ΔABC is either a right angled or an isosceles triangle.

If the angles A, B, C of ΔABC are in A.P. and its sides a, b, c are in G.P., then show that a², b², c² are in A.P.

Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`

Find the separate equations of the lines represented by the equation 3x² – 10xy – 8y² = 0.